German Patent No. 195 00 706 describes a fuel injector. In this context, provision is made for a lift translator or travel transformer which converts a relatively small actuator travel, for example, of a piezoelectric actuator, into a longer lift of the valve needle. In this context, the expansion of the actuator is introduced into an amplifier chamber via a working piston of the lift translator, and transmitted to the valve needle via a lift piston, the valve executing a lift which is increased in the ratio of the piston areas bordering the amplifier chamber at the end faces. To compensate for temperature influences, wear, and manufacturing tolerances on the actuator travel, the amplifier chamber is provided with a defined leak, which is implemented by a ring gap between the piston and a valve-housing wall, and has a sufficiently high resistance to flow so that the movements of the actuator are transmitted to the valve needle in an essentially undamped manner. Used as hydraulic medium of the lift transmission is the fuel itself, diesel fuel in the case of German Patent No. 195 00 706. However, this creates the problem that the defined leak must be very small because of the low viscosity of the fuel. If the intention is for the known fuel injector to be used for Otto spark ignition engines, the further problem arises that the gasoline boils at comparatively low temperatures and can then no longer work as hydraulic medium because of the formation of bubbles.